Home > Uncategorized > The Keynes-Ramsey-Savage debate on probability

The Keynes-Ramsey-Savage debate on probability

from Lars Syll

Mainstream economics nowadays usually assumes that agents that have to make choices under conditions of uncertainty behave according to Bayesian rules, axiomatized by Ramsey (1931) and Savage (1954) — that is, they maximize expected utility with respect to some subjective probability measure that is continually updated according to Bayes theorem. If not, they are supposed to be irrational, and ultimately – via some “Dutch book” or “money pump”argument – susceptible to being ruined by some clever “bookie”.

Bayesian Stats Joke | Data science, Mathematik meme, Mathe witzeBayesianism reduces questions of rationality to questions of internal consistency (coherence) of beliefs, but – even granted this questionable reductionism – do rational agents really have to be Bayesian? As I have been arguing elsewhere (e. g. herehere and here) there is no strong warrant for believing so.

In many of the situations that are relevant to economics one could argue that there is simply not enough of adequate and relevant information to ground beliefs of a probabilistic kind, and that in those situations it is not really possible, in any relevant way, to represent an individual’s beliefs in a single probability measure.

Say you have come to learn (based on own experience and tons of data) that the probability of you becoming unemployed in Sweden is 10 %. Having moved to another country (where you have no own experience and no data) you have no information on unemployment and a fortiori nothing to help you construct any probability estimate on. A Bayesian would, however, argue that you would have to assign probabilities to the mutually exclusive alternative outcomes and that these have to add up to 1, if you are rational. That is, in this case – and based on symmetry – a rational individual would have to assign probability 10% to becoming unemployed and 90% of becoming employed.

That feels intuitively wrong though, and I guess most people would agree. Bayesianism cannot distinguish between symmetry-based probabilities from information and symmetry-based probabilities from an absence of information. In these kinds of situations most of us would rather say that it is simply irrational to be a Bayesian and better instead to admit that we “simply do not know” or that we feel ambiguous and undecided. Arbitrary an ungrounded probability claims are more irrational than being undecided in face of genuine uncertainty, so if there is not sufficient information to ground a probability distribution it is better to acknowledge that simpliciter, rather than pretending to possess a certitude that we simply do not possess.

I think this critique of Bayesianism is in accordance with the views of John Maynard Keynes’ A Treatise on Probability (1921) and General Theory (1937). According to Keynes we live in a world permeated by unmeasurable uncertainty – not quantifiable stochastic risk – which often forces us to make decisions based on anything but rational expectations. Sometimes we “simply do not know.” Keynes would not have accepted the view of Bayesian economists, according to whom expectations “tend to be distributed, for the same information set, about the prediction of the theory.” Keynes, rather, thinks that we base our expectations on the confidence or “weight” we put on different events and alternatives. To Keynes expectations are a question of weighing probabilities by “degrees of belief”, beliefs that have preciously little to do with the kind of stochastic probabilistic calculations made by the rational agents modeled by Bayesian economists.

Stressing the importance of Keynes’ view on uncertainty John Kay writes in Financial Times:

For Keynes, probability was about believability, not frequency. He denied that our thinking could be described by a probability distribution over all possible future events, a statistical distribution that could be teased out by shrewd questioning – or discovered by presenting a menu of trading opportunities. In the 1920s he became engaged in an intellectual battle on this issue, in which the leading protagonists on one side were Keynes and the Chicago economist Frank Knight, opposed by a Cambridge philosopher, Frank Ramsey, and later by Jimmie Savage, another Chicagoan.

Keynes and Knight lost that debate, and Ramsey and Savage won, and the probabilistic approach has maintained academic primacy ever since …

I used to tell students who queried the premise of “rational” behaviour in financial markets – where rational means are based on Bayesian subjective probabilities – that people had to behave in this way because if they did not, people would devise schemes that made money at their expense. I now believe that observation is correct but does not have the implication I sought. People do not behave in line with this theory, with the result that others in financial markets do devise schemes that make money at their expense.

Although this on the whole gives a succinct and correct picture of Keynes’s view on probability, I think it’s necessary to somewhat qualify in what way and to what extent Keynes “lost” the debate with the Bayesians Frank Ramsey and Jim Savage.

In economics it’s an indubitable fact that few mainstream neoclassical economists work within the Keynesian paradigm. All more or less subscribe to some variant of Bayesianism. And some even say that Keynes acknowledged he was wrong when presented with Ramsey’s theory. This is a view that has unfortunately also been promulgated by Robert Skidelsky in his otherwise masterly biography of Keynes. But I think it’s fundamentally wrong. Let me elaborate on this point (the argumentation is more fully presented in my book John Maynard Keynes (SNS, 2007)).

It’s a debated issue in newer research on Keynes if he, as some researchers maintain, fundamentally changed his view on probability after the critique levelled against his A Treatise on Probability by Frank Ramsey. It has been exceedingly difficult to present evidence for this being the case.

Ramsey’s critique was mainly that the kind of probability relations that Keynes was speaking of in Treatise actually didn’t exist and that Ramsey’s own procedure  (betting) made it much easier to find out the “degrees of belief” people were having. I question this both from a descriptive and a normative point of view.

What Keynes is saying in his response to Ramsey is only that Ramsey “is right” in that people’s “degrees of belief” basically emanates in human nature rather than in formal logic.

Patrick Maher, former professor of philosophy at the University of Illinois, even suggests that Ramsey’s critique of Keynes’s probability theory in some regards is invalid:

Keynes’s book was sharply criticized by Ramsey. In a passage that continues to be quoted approvingly, Ramsey wrote:

“But let us now return to a more fundamental criticism of Mr. Keynes’ views, which is the obvious one that there really do not seem to be any such things as the probability relations he describes. He supposes that, at any rate in certain cases, they can be perceived; but speaking for myself I feel confident that this is not true. I do not perceive them, and if I am to be persuaded that they exist it must be by argument; moreover, I shrewdly suspect that others do not perceive them either, because they are able to come to so very little agreement as to which of them relates any two given propositions.” (Ramsey 1926, 161)

I agree with Keynes that inductive probabilities exist and we sometimes know their values. The passage I have just quoted from Ramsey suggests the following argument against the existence of inductive probabilities. (Here P is a premise and C is the conclusion.)

P: People are able to come to very little agreement about inductive proba- bilities.
C: Inductive probabilities do not exist.

P is vague (what counts as “very little agreement”?) but its truth is still questionable. Ramsey himself acknowledged that “about some particular cases there is agreement” (28) … In any case, whether complicated or not, there is more agreement about inductive probabilities than P suggests …

I have been evaluating Ramsey’s apparent argument from P to C. So far I have been arguing that P is false and responding to Ramsey’s objections to unmeasurable probabilities. Now I want to note that the argument is also invalid. Even if P were true, it could be that inductive probabilities exist in the (few) cases that people generally agree about. It could also be that the disagreement is due to some people misapplying the concept of inductive probability in cases where inductive probabilities do exist. Hence it is possible for P to be true and C false …

I conclude that Ramsey gave no good reason to doubt that inductive probabilities exist.

Ramsey’s critique made Keynes more strongly emphasize the individuals’ own views as the basis for probability calculations, and less stress that their beliefs were rational. But Keynes’s theory doesn’t stand or fall with his view on the basis for our “degrees of belief” as logical. The core of his theory — when and how we are able to measure and compare different probabilities —he doesn’t change. Unlike Ramsey he wasn’t at all sure that probabilities always were one-dimensional, measurable, quantifiable or even comparable entities.

  1. January 24, 2021 at 9:03 pm

    This article says, “In economics it’s an indubitable fact that few mainstream neoclassical economists work within the Keynesian paradigm.”

    Nevertheless, they usually work within the ‘reconciliation’ paradigm Sir John Hick’s constructed in his 1937 paper “Mr. Keynes and the ‘Classics'”, in effect casting elements of Keyne’s General Theory into a framework which rescued the neoclassical economics of his day. If one examines the many directions economic theory has taken since that paper by Sir John Hicks, they all suffer the fault that people continue, in the framework, to use ‘scarce’ means to pursue psychological ends.

    As Keynes wrote later to Joan Robinson, “I am not a Keynesian.” He wrote that because the recasting the General Theory –more his early thoughts about what made for aggregate demand than a well-developed theoretic– into a neoclassical framework of the time not only was not at all descriptive of those early thoughts but also constituted a misdirection –one which preserved the irrelevance of neoclassicism {a dead-end theoretic searching for reasons why its predictions consistently fail to describe economic realities and are always well off-the-mark of economic trajectories. From asymmetric information, to transactions costs, to new-fangled ‘bounded rationality’, neoclassical economists seek to preserve their dead-ended theoretic by coming up with this or that ‘explanation’ for the failure of their predictions, when it is the theoretic itself which is structurally unfounded.

  2. shivz
    January 25, 2021 at 10:30 am

    “Fortune is the arbiter of one-half of our actions” (Machiavelli). If you can quantify this, you master probability.

  3. January 25, 2021 at 10:34 am

    I learned of this debate through Passmore’s “A Hundred Years of Philosophy”, Penguin, 1968, p.345-7. Reading that again, it confirms not only that my own reasoning about probability agrees with Keynes’s, but that Keynes (a) rejects Hume’s “black ball” paradigm (which the “frequentists” Venn and Ramsey take for granted); (b) he sees it (as I see its role in scientific method) as “confirmation theory”; (c) we apprehend it intuitively (as I argue, “with the right side of the brain”); (d) it is always relative (involving comparison, e.g. of analog right-brain reasoning with left-brain digital reasoning); (e) involves a preference for “matters of fact”.

    How I came to understand this was from the example of throwing dice. If the dice has six faces then intuitively the probability of it landing on any one of them is 1/6, but this assumes it is unbiassed. To confirm that one can trial it by throwing it a large number of times and using the left brain to calculate whether the outcome calculated that way is the same within a formal tolerance determined from the number of trials not being infinite.

    Applied to share prices, Ramsey was betting on average the prices going up, whereas Keynes would want to confirm that the changes reflected the actual performance of the firm.

  4. January 26, 2021 at 8:23 am

    Interesting. Thank you.

  5. Gerald Holtham
    January 28, 2021 at 7:10 pm

    People generally “just don’t know” what is going to happen. Yet they often take action. Why and how do they do it? Keynes was surely right to suppose that businessmen did not decide on investment on the basis of fine calculations of discounted cash flow. But his answer was “animal spirits” which is no answer at all.
    People make bets on the basis of certain assumptions and judgements that some outcomes are more likely than others. It requires empirical research, not philosophical speculation, to learn how people do that and to see whether there are general tendencies in a given population.
    Such empirical research as we have tends to confirm that people do not learn in a Bayesian way. In controlled environments it has been found that the way people revise expectations is generally inferior to Bayesian learning. As John Kay noted, people make mistakes.
    The use of Bayesian techniques in analysing a quantitative data set is a well-established procedure. It does not imply that people whose behaviour generated the data were behaving on Bayesian principles. Most people have only a hazy grasp of statistics so one should not rely on theories that suppose they are statistical wizards. They are not – but that does not invalidate the use of statistics in analysis.

    • January 29, 2021 at 10:47 am

      Gerald is missing the point that the view of Bayesianism being taught is that of the Ramsey rather than the Keynesian school. It is that which invalidates the current use of statistics in analysis: it is seeking agreement on what people say they observed rather than the coincidence, of a measure agreed on that way, with reality observed in a completely different way. What I’ve not been able to confirm is whether Bayes himself was thinking of probability in terms of Hume’s drawing black or white billiard balls from a bag, or of throwing a dice and seeking confirmation it was unbiassed by sampling the outcomes of throwing it.

      Incidentally, Gerald is again using either/or logic to dismiss Keynes’ argument that some (not all) speculators base their decisions on (in Myers-Briggs terms) feelings, for which “animal spirits” – though just a figure of speech – is suggestive of what animals have that motivates their “fight or flight” responses. That is actually a very reasonable answer, even if Keynes’s intuitive inference slips through the cracks in Gerald’s left-brain, word-oriented deductive logic.

  6. Gerald Holtham
    February 4, 2021 at 3:44 pm

    Keynes was guilty of implicit theorising because “animal spirits” are not observed except in the actions they are supposed to explain. Therefore they are not an answer to any useful question.
    Keynes treated expectations as exogenous. This left a hole filled, disastrously, by the rational expectations crowd. The answer to understanding expectations formation under conditions of uncertainty is to go out and study behaviour, verbal and actual. We don’t get anywhere sitting in armchairs trading prejudices.

    • Yoshinori Shiozawa
      February 5, 2021 at 3:09 am

      Gerald, I have a question. You put it:

      Such empirical research as we have tends to confirm that people do not learn in a Bayesian way. In controlled environments it has been found that the way people revise expectations is generally inferior to Bayesian learning. As John Kay noted, people make mistakes.

      I agree that people do not learn in a Bayesian way. But is that mean that people make mistakes as John Kay judged it? “Controlled environment” is just a specific situation conceived from probability theory. Probably, a case where there is a fixed probability for a set of events. But, in a more often experienced (real life) situation, it is doubtful even if a probability is determined at all. Controlled experiments already implicitly assume a situation that can be suitably interpreted by probability theory. I admit that the life is full of situations we cannot know in a deterministic way. Probability theory is just one of possible theories that can treat such situations. However, how can we claim that there are no other situations that can be more usefully treated with other (probably not yet created) theories? It seems for me that the problem setting that assumes situations are either deterministic or probabilistic contains already something wrong.

      I agree with Gerald that animal spirits are no answer at all. So, my question is independent from Keynes’s animal spirit problem.

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